How to kill epsilons with a dagger: a coalgebraic take on systems with algebraic label structure

We propose an abstract framework for modeling state-based systems with internal behavior as e.g. given by silent or ϵ-transitions. Our approach employs monads with a parametrized fixpoint operator † to give a semantics to those systems and implement a sound procedure of abstraction of the internal transitions, whose labels are seen as the unit of a free monoid. More broadly, our approach extends the standard coalgebraic framework for state-based systems by taking into account the algebraic structure of the labels of their transitions. This allows to consider a wide range of other examples, including Mazurkiewicz traces for concurrent systems.Funded by the ERDF through the Programme COMPETE and by the Portuguese Foundation for Science and Technology, project ref. FCOMP-01-0124-FEDER-020537 and SFRH/BPD/71956/2010. Acknowledge support by project ANR 12IS0 2001 PACE